Point Pattern Analysis on a Sphere

This thesis develops statistical methodology for analysing spatial patterns of points on a sphere. The main results include relevant theory, methods for estimating point process intensity and summary functions such as Ripley's K function, methods for plotting these estimates which have useful properties, and models on the sphere such as the analogue of the Neyman­-Scott cluster process. These methods are implemented in code in a software package, and which have been used to analyse the spatial pattern of galaxies. Other possible applications include analysis of initiation points of cyclones, and locations of meteorite impacts, on the Earth's surface.